Calculating the Pearson correlation coefficient can be complicated but software makes it much easier. You can use several methods to calculate correlation in Excel.

Stuart R. Lipsitz, Traci Leong, Joseph Ibrahim, Steven Lipshultz, A Partial Correlation Coefficient and Coefficient of Determination for Multivariate Normal Repeated Measures Data, Journal of the ...

Time varying correlations are often estimated with multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models that are linear in squares and cross products of the data. A ...